The English side extended their perfect run this season to 11 matches, but only after seeing off a battling display from Heineken Cup debutants at Twickenham Stoop.
The Irish outfit scored two tries through Tiernan O'Halloran and former Quins full-back Gavin Duffy but 20 points from the boot of Nick Evans and Karl Dickson's score saw the hosts claim victory.
"This Connacht team will give nothing to anyone in the Heineken Cup," O'Shea said.
"They came at us absolutely full metal jacket but we knew what was coming. Nobody in our dressing room is arrogant enough to believe you get things for free.
"But we had the fortitude to come through and found a way to win. Connacht played really good rugby in the second half but, mentally, our guys are very strong."
Former All Blacks fly-half Evans kicked six penalties and a conversion to see Harlequins home and O'Shea predictably heaped praise on him.
He said: "His game management was outstanding. Defensively he's got better and his kicking percentages have gone up."
The only negatives for Harlequins were serious-looking injuries to centre George Lowe and lock Ollie Kohn.
"Lowe hurt his ankle and Kohn had a nasty bicep injury. They could both be out for a while," said O'Shea, who had words of consolation for Connacht.
"They will go away disappointed to get nothing out of the game but they should be proud of what they've done tonight."
Connacht head coach Eric Elwood was full of praise for his own side but admitted that coming away from the clash without even a losing bonus point was hard to take.
"It's a hard pill to swallow," he said.
"The most frustrating and disappointing thing is that for all the effort, endeavour, commitment and hard work we have actually come away from The Stoop with nothing.
"The game was in the balance at 19-17 when we had a crucial scrum and you think you have a chance so we've a disappointed changing room."
Elwood revealed that Connacht's former Harlequins full-back Duffy was in tears after his old side survived intense second-half pressure to hang on for victory.
"Obviously there's the connection with Harlequins and he's hurting pretty badly," he added.
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